Download Estimating How Much Sea Level Changes when

SSAC2006.QE697.PB1.2
Global Climate: Estimating How Much Sea Level
Changes when Continental Ice Sheets Form
Core Quantitative Issue
Estimation
Over the last few million years, Earth
has experienced numerous ice ages
when vast regions of the continents
were glaciated and sea level was lower
as a result.. How much did sea level
drop during these glaciations?
Supporting Quantitative Issues
Number sense: Significant figures
Algebra: Manipulating of equations
Geometry: circle: area
Geometry: sphere: surface area
Prepared for SSAC by
Paul Butler – The Evergreen State College, Olympia, WA 98505
© The Washington Center for Improving the Quality of Undergraduate Education. All rights reserved. 2006
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Overview
At times during the Quaternary Period (approximately the last 2 million
years of Earth history), glaciers were much more extensive than they are
now. The world’s ocean was the source of the glacial ice, and so sea
level was significantly lower when the additional ice was present. As
Earth still has a significant amount of ice, primarily in Greenland and
Antarctica, large-scale melting of that ice would result in a significant
sea-level rise. It is possible to estimate the amount of sea-level rises
and falls by estimating the changes in ice volumes on land. Changes in
the amount of floating ice do not affect sea level (why?).
•Slide 3 states the problem and discusses assumptions, estimation and
significant figures.
•Slide 4 shows how to estimate the surface area of world oceans.
•Slide 5 shows how to estimate sea-level drop during glacial maxima.
•Slides 6 - 8 evaluate the effect of one of the underlying assumptions.
•Slides 9 and 10 give the assignment to submit to your instructor.
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The Problem
How much did global sea-level drop during the last glacial
maximum, when there was an estimated 70×106 km3 of ice?
A Word about Assumptions, Estimation, and Significant Figures
In order to investigate the relationship between ice volume and sea-level, we
need to make a few assumptions and use some estimates of the magnitude of
quantities in the geological past. In general in such calculations, the estimates
are commonly accepted values, not wild guesses; the estimates are thought to
be correct to within 5 to 10%. The assumptions are made to simplify the
process of calculation, including the equations that one would use. Common
assumptions include: (1) not taking account of factors that have a minor effect,
and (2) using simple, rather than complicated, geometries.
In this estimation calculation, we will ignore the changes in water volume due to
thermal expansion and contraction. We will also ignore the effects of grounded
ice. And, we will work with circular ocean basins. With these assumptions, we
will often work with only three significant figures.
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Determining the surface area of Earth’s oceans
Although Earth is not a perfect sphere, it is routine in calculations such as
this one to consider Earth to be a sphere with an average radius of
approximately 6370 km. In addition, you may recall that oceans cover
approximately 71% of Earth’s surface.
Recreate the spreadsheet below to calculate the surface area of Earth’s
oceans. The surface area of a sphere (A) with radius (r) = 4πr2.
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B
Earth's radius
Earth's surface area
from formula
scientific notation
Earth's ocean area (%)
Earth's ocean area (km2)
from formula
scientific notation
C
D
6370 km
509904363.8 km2
5.10E+08 km2
71%
362032098.3 km2
3.62E+08 km2
Estimate of
Earth’s surface
area, to three
significant
figures.
Estimate of the
area of Earth’s
oceans, to three
significant figures.
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Estimating global sea-level drop at glacial maxima
As a first approximation, continents and ocean basins can be modeled as if the
shoreline is like a seawall, i.e. the interface of land and water does not migrate
laterally as sea level changes. We will check that assumption shortly.
Recreate the spreadsheet below to calculate the drop in sea level if the
ice volume at the last glacial maximum was 70 million km3, in contrast to
the current volume of 25 million km3.
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B
C
D
Ice volumes
at glacial maxima 70000000 km3
current volume 25000000 km3
difference 45000000 km3
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3.62E+08 km
Earth's ocean area
Decrease in sea-level
directly from formula 1.24E-01 km
conversion to meters
124 m
Note: Estimates of
sea-level drop
during the last
glacial maximum
using more
sophisticated
models range from
100 – 135 m.
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Evaluate the assumption that the shoreline does not migrate during sea-level change
To evaluate the assumption of a non-migrating shoreline, we need to estimate the
area of the continental shelves as a percentage of the area of the ocean basins. If
this percentage is small, then the “seawall” assumption should not create a
significant error in our estimate of sea-level decrease. As the continental shelf
extends to an average depth of 150 m (greater than the drop in sea level
associated with the glacial maxima), we need not be concerned with the
continental slope. The average width of the continental shelf is about 70 km.
Hint: Here is a model for
a flat, circular ocean
basin and continental
shelf. A circle with
radius r1 encompasses
the entire basin. A circle
of radius r2 represents
the area of the ocean
basin, minus the area of
the continental shelf.
(The map is not to
scale).
r2
r1
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Evaluate the assumption that the shoreline does not migrate during sea-level change, 2
Recreate the spreadsheet below to estimate the area of the continental
shelf assuming that the Earth is flat and the world’s major ocean basins
are circular (as diagramed on the previous slide).
Hint: The formula for the area of a circular ocean basin on a flat Earth is: A =
π r2. Given the area of each ocean basin in Column C, solve the equation for
the radius (r) and use it to find the radius of the basin models (Col. E), and
then the area of the shelf (Col. F). For the area of the shelf, recall that the
average width of the shelf is 70 km.
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B
C
D
E
F
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2
Ocean Area (km ) % world total Ocean radius (r ) Shelf area (km )
Pacific
155557000
46.3%
7037
3079514
Atlantic
76762000
22.8%
4943
2158689
Indian
68556000
20.4%
4671
2039199
Southern
20327000
6.1%
2544
1103373
Arctic
14056000
4.2%
2115
914929
335258000
99.8%
9295705
Total
2.8%
Estimate of shelf area
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Evaluate the “sea wall” assumption based on the estimate of shelf area
Examine the hypsographic curve show in the figure below.
Trujillo, Alan P.; Thurman, Harold V., Essentials of Oceanography, 8th Edition, (c)2005. Electronically reproduced by permission of Pearson Education, Inc., Upper Saddle River, New Jersey.
As the area of the continental shelf is small, relative to the size of the ocean
basins, the “sea-wall” assumption does not appear to have a significant impact.
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Summary
•We estimated the area of the oceans based on the fact that the surface area of
the Earth is comprised of 71% ocean.
•Using estimates of the total ice volume during the glacial maxima and what
exists today, we approximated the change in sea level by dividing the change in
ice volume by the total ocean area.
•Our sea level change estimation falls within the range of estimates given by
modeled results.
•By showing that the total area of continental shelves is only ~2% of the total
oceanic area, we determined that our “seawall” assumption is acceptable for
our estimate of sea level change.
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End of Module Assignment
1.
In the estimate for sea-level drop at glacial maxima, in order to assess the
assumption that the shape of the continental shelf could be ignored, oceans
were modeled as circles. Now, you will model the continental shelf as if it was
attached to flat, circular continents. (Areas of the continents at present sealevel are given in the table below to three significant figures.) How does this
value compare to what was determined for “circular” oceans, i.e. does it
confirm or confound what you determined earlier?
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A
B
Continent
Area (km2)
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Eurasia
54200000
3
Africa
30400000
4
North America
24500000
5
South America
17800000
6
Antarctica
13700000
7
Oceania (inc. Australia)
9010000
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End of Module Assignment (continued)
2.
Currently, there is approximately 25 × 106 km3 of ice on Earth’s surface.
Using techniques developed in this module, estimate the sea-level change
that would result from melting all of this ice.
3.
In describing sea-level change associated with increased ice volume during
glacial maxima, the configuration of the continental shelf was simplified.
Continents were modeled as if their shorelines below modern sea level were
vertical cliffs. It was shown that this did not add significant error to the
estimation. Is this assumption reasonable for rising sea level? Explain.
4.
During the last glacial maximum (about 20,000 years ago), approximately
30% of Earth’s land surface was covered by ice. Calculate the average
thickness of the ice. Use the glacial maximum ice volume given earlier in the
module. Explain why the value that you calculate is likely too high.
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